Question
Mon March 12, 2012 By:

variation of g

Expert Reply
Tue March 13, 2012
At a given place, the value of acceleration due to gravity is constant but it varies from one place to another place on the earth surface. It is due to this fact that earth is not a perfect sphere. It is flattened at the poles and bulges out at the equator (Ellipsoidal shaped) see fig. below.

 

acceleration-due-to-gravity-91

In the above figure, the polar radius, Rp is not equal to the equatorial radius, Re. Now,

acceleration-due-to-gravity-101

Now, as ‘G’ & ‘M’ remain constant, therefore,

acceleration-due-to-gravity-111

Thus, the value of ‘g’ is minimum at the equator and maximum at the poles. It means, ‘g’ increases as we go from equator to pole.
The value of acceleration due to gravity also varies with altitude, depth and rotation of the earth.

1) If a body is taken above the surface of earth, the value of acceleration due to gravity varies inversely as the square of the distance from the centre of the earth. But if the body is taken inside the earth, acceleration due to gravity decreases linearly with distance from the centre of earth.

It becomes clearer by the graph below.

acceleration-due-to-gravity-121

The part AB of the graph shows the variation of ‘g’ with height ‘h’ above the surface of earth because, at height ‘h’, change in gravity is given by

acceleration-due-to-gravity-131

It means,

acceleration-due-to-gravity-141

where r = R+h. Thus the variation of g and r is a parabolic curve.

Similarly, the variation in ‘g’ with depth is given by

acceleration-due-to-gravity-151

That is,

acceleration-due-to-gravity-161

Thus the variation of ‘g’ and ’d’ is a straight line shown in graph by line AC.

2) If the rate of rotation of earth increases, the value of acceleration due to gravity decreases at all places on the surface of earth except at poles where it remains constant.

3) If earth stops rotating on its axis, there will be increase in the value of acceleration due to gravity at equator, but there will be no change in the value of ‘g’ at poles.

4) The rate of decrease of the acceleration due to gravity with height is twice as compared to that with depth.

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